Variable chirp optical modulator having different length electrodes

ABSTRACT

A variable chirp optical modulator is provided. An optical waveguide is split for part of its length into first and second waveguide arms. Electrode pairs are positioned to be proximate a first portion of corresponding waveguide arms. The lengths of each of the electrodes are different and are selected to provide a predetermined level of chirp.

This invention pertains to optical systems, in general, and to optical modulators for use in optical systems in particular.

BACKGROUND OF THE INVENTION

The term “optical system” as used herein refers to any system that utilizes light waves to convey information between one node and one or more other nodes. Much of the optical communications network in place utilizes optical fibers. One property of optical fibers that is of concern is dispersion. Dispersion in optical fiber occurs as a result of variation in the refractive index of the optical fiber with wavelength. Modulation of an optical signal results in optical harmonics of the modulation frequency about the carrier frequency. When modulated light is passed through a length of optical fiber that exhibits chromatic dispersion, the phase of the light at the distal end of the fiber varies as a function of its frequency thus producing phase modulation. Detection of optical signals causes mixing of the various frequency components, but because the various frequency components have differing phases, the mixing results in the amplitude of the detected signal changing on account of the linewidth of the transmitted signal.

In other words, in a dispersive medium, different wavelengths of light travel at slightly different velocities. This causes optical pulses to broaden in wavelength as they travel down optical fiber links, causing difficulty at a receiver when reconstructing an electrical pulse from a received optical pulse. With the advent of erbium doped fiber amplifiers, longer distances are traversed over optical fiber. The problems caused by dispersion are referred to as “chirping”. Chirping becomes increasingly more significant of a problem at higher modulation frequencies such as frequencies at 10 GHz and above. One limiting factor on the length of links in long haul transmission of optical signals is chromatic dispersion that occurs because a transmitter has a real optical linewidth and the refractive index of optical fiber varies, dependent upon the wavelength of the optical signals. Optical linewidth of a transmitter is determined by two factors. The factors are the inherent linewidth at DC and the broadening of the linewidth introduced by modulation. Broadening of the linewidth introduced by modulation is referred to as “static” chirp. Other optical components may introduce a shift to the center frequency of the optical linewidth; this is referred to as dynamic chirp.

Static and dynamic chirp introduce a pulse width change or phase modulation and an amplitude shift or intensity modulation in the optical signal. The intensity modulation changes are such that there may be a combination of link length, dispersion and frequency that completely nulls out the signal to be detected. In the case of pulse width changes, positive dynamic chirp will broaden the width of a pulse propagating down a fiber and negative dynamic chirp will narrow the pulse. Either of the two effects can render a modulated signal undetectable.

The chirp effects can be compensated for by deliberate introduction of an offsetting chirp in modulated signals. Various modulators providing controlled chirp have been described in the prior art. Typically such modulators are based upon designs that form the modulator on a substrate. The substrate material is frequently lithium niobate (LiNbO₃) although other electro-optic materials may be used.

The electro-optic effect in LiNbO₃ depends on the direction of the electric field relative to the orientation of the crystalline structure of the substrate along which the optical wave propagates. In an orientation referred to as an “X-cut” the optic axis is parallel to the plane of the substrate and at right angles to the direction of propagation of the optical wave, In an orientation referred to as “Z-cut” the optic axis is normal to the plane of the substrate.

SUMMARY OF THE INVENTION

An optical modulator in accordance with the invention includes an optical waveguide that splits for part of its length into first and second waveguide arms, with the waveguide arms recombining to an output waveguide portion. A first electrode proximate the first waveguide arm subjects a first optical length of said first waveguide to a first modulating electric field. A second electrode proximate the second waveguide arm subjects a first optical length of said second waveguide arm to a second modulating electric field. In accordance with the principles of the invention, the length of the second electrode is shorter that the first length of the first electrode. The lengths of the first and second electrodes are selected to provide a predetermined amount of chirp.

In one embodiment of the invention, the first electrode is one electrode of a first electrode pair proximate said first waveguide arm. The electrodes of the first electrode pair are arranged with respect to each other and the first waveguide arm to subject a first optical length of said first waveguide to a first modulating electric field. The second electrode is one electrode of a second electrode pair proximate the second waveguide arm. The electrodes of the second electrode pair are arranged with respect to each other and to said second waveguide arm to subject a first optical length of said second waveguide arm to a second modulating electric field, the second electrode pair is shorter than the first electrode pair. In accordance with the principles of the invention, the lengths of each of the first electrode pair and the second electrode pair are selected to provide a predetermined amount of chirp.

In accordance with one aspect of the invention, the first electrode pair and the second electrode pair share a common electrode.

In accordance with another aspect of the invention, the gap between the first electrode pair is equal to the gap between the second electrode pair in the regions in which the first and second waveguide arms are subjected to the first and second electric fields, respectively.

In accordance with the principles of the invention, the amount of chirp provided by the modulator is varied from a fixed chirp by varying the power split between the two waveguide arms, and/or the voltage applied to the first and second electrodes and/or a bias voltage applied to bias electrodes.

BRIEF DESCRIPTION OF THE DRAWING

The invention will be better understood from a reading of the following detailed description in conjunction with drawing, in which like reference designations in the various drawing figures are used to identify like elements, and in which:

FIG. 1 illustrates a portion of a prior art integrated optic Mach Zehnder Interferometer modulator;

FIG. 2 is a partial cross-section of the prior art device of FIG. 1;

FIG. 3 illustrates a second prior art integrated optic modulator;

FIG. 4 is a partial cross-section of the prior art device of FIG. 3;

FIG. 5 depicts an integrated optic modulator in accordance with the principles of the invention;

FIG. 6 is a partial cross-section of the modulator of FIG. 5;

FIG. 7 illustrates the optical waveguide paths of a Mach Zehnder Interferometer modulator in accordance with the invention;

FIG. 8 illustrates a second integrated optic modulator in accordance with the principles of the invention;

FIG. 9 is a partial cross section of the modulator of FIG. 8 taken along lines 9—9;

FIG. 10 illustrates a third integrated optic modulator in accordance with the principles of the invention;

FIG. 11 is a partial cross-section of the modulator of FIG. 10 taken along lines 11—11

FIG. 12 illustrates a fourth integrated optic modulator in accordance with the invention;

FIG. 13 is a partial cross-section of the modulator of FIG. 12 taken along lines 13—13; and

FIG. 14 is a partial cross-section of the modulator of FIG. 12 taken along lines 14—14.

DETAILED DESCRIPTION

Turning now to FIG. 1, a portion of a prior art integrated optic Mach Zehnder Interferometer modulator 10 is shown. Mach Zehnder Interferometer type modulators are typically utilized in prior modulator designs. A Mach Zehnder Interferometer modulator configuration comprises an optical waveguide splitter coupled to two waveguide arms and a waveguide combiner. Electrodes are associated with each of the two waveguide arms and provide a modulation voltage to one or both electrodes. The modulation voltages change the optical index of the waveguide arms and thereby change the relative phase of the two light beams. A differential phase change may result in both beams combining in phase to give a maximum intensity signal. This is the “on” state. A λ/2 degree phase shift difference results in beam extinction or an “off” state. Chirp can be created by uneven modulation between the two waveguide arms of the Mach Zehnder Interferometer modulator.

The Intensity Modulation effect Vpi is the voltage differential between the Mach Zehnder Interferometer modulator electrodes. A trade off between the intensity modulation effect and the amount of chirp is required. That is, larger chirp requires a higher Vpi

Modulator 10 includes an optical waveguide 12 that is split by an optical splitter 14 into two waveguide arms 16, 18. Optical waveguide arms 16, 18 are rejoined with an optical coupler 20. FIG. 2 shows modulator 10 in cross section. The modulator is formed on a substrate 1 that is typically lithium niobate. Optical waveguide arms 16, 18 are formed in substrate 1. Electrodes 22, 24, 26 are formed on substrate 1 proximate optical waveguide arms 16, 18. The distance between electrode 22 and electrode 24 is different from the distance between electrode 24 and electrode 26, providing uneven gaps 28, 30 between electrode pairs. This approach is utilized in the integrated optical modulator of U.S. Pat. No. 6,052,496.

A second prior art integrated optic Mach Zehnder Interferometer modulator 210 is shown in FIGS. 3 and 4. Modulator 310 includes an optical waveguide 312 that is split by an optical splitter 314 into two waveguide arms 316, 318. Optical waveguide arms 316, 318 are rejoined with an optical coupler 320. FIG. 4 shows modulator 310 in cross section. The modulator is formed on a substrate 301 that is typically lithium niobate. Optical waveguide arms 316, 318 are formed in substrate 301. Electrodes 322, 324, 326 are formed on substrate 301 proximate optical waveguide arms 316, 318. One waveguide arm 318 is disposed such that the adjacent electrodes 322, 324 are located on either side of waveguide arm 318. Electrode 326 is disposed above optical waveguide arm 318. The distance between the electrode pair comprising electrode 322 and electrode 324 is the same as the distance between the electrode pair comprising electrode 324 and electrode 326, providing even gaps 328, 330 between electrode pairs.

Turning now to FIGS. 5 and 6, the approach in accordance with the present invention is illustrated. In accordance with the invention, an integrated optic modulator 510 includes an optical waveguide 512 that is split by an optical splitter 514 into two waveguide arms 516, 518. Optical waveguide arms 516, 518 are rejoined with an optical coupler 520. FIG. 6 shows modulator 510 in cross section. The modulator 510 is formed on a substrate 501 that is lithium niobate. As will be appreciated by those skilled in the art, substrate 501 may be of other material including, but not limited to LiTaO₃. Optical waveguide arms 516, 518 are formed in substrate 501. Electrodes 522, 524, 526 are formed on substrate 501 proximate optical waveguide arms 516, 518. The electrodes 522, 524, 526 are arranged to form two electrode pairs with electrode 524 being a common electrode in the two electrode pairs. That is, electrodes 222, 224 form one electrode pair and electrodes 224, 226 form another electrode pair. The distance between electrode 522 and electrode 524 is the same as the distance between electrode 524 and electrode 526, providing even gaps 528, 530 between electrode pairs. However, in contrast to the prior art approach of the device of FIGS. 1 and 2, electrode 526 is a different length than electrode 522.

LiNbO₃ substrate modulators used to perform intensity modulation can in general also impress a phase modulation on an optical signal. The degree of phase modulation is expressed as the chirp parameter $\begin{matrix} {\alpha \equiv \frac{\frac{\varphi}{t}}{\frac{1}{2}\frac{I}{t}}} & (1) \end{matrix}$

where φ is the phase shift imparted to the output signal and I is the intensity of the light output.

The most common intensity modulator using lithium niobate is the Mach Zehnder Interferometer modulator. Turning now to FIG. 7, only the optical path or a Mach Zehnder Interferometer is shown. The optical waveguide 712 is split by splitter or “y” 714 into two waveguide arms 716, 718 that rejoin at coupler 720. The input signal at an amplitude A_(i) is split into two signals of respective amplitudes ρA_(i) and σA_(i) which propagate along the lengths L₁ and L₂ of waveguide arms 716, 718 before being recombined. The lengths L₁, L₂ are the optical path lengths due to intrinsic characteristics of the waveguide arms and any applied electrode voltages. Coupler 720 combines the signals on the two waveguide arms 716, 718. The intensity of the light in each arm is equal. The combined output amplitude, A, is the output amplitude of the optical signals in each waveguide arm 716, 718. The output amplitudes for signals on the two waveguide arms 716, 718 are “r” and “s”, respectively, with $\begin{matrix} {{r = {\frac{\sqrt{2}}{2}A_{i}\rho \quad ^{{({{\omega \quad t} - {kL}_{1}})}}}},\quad {and}} & (2) \\ {s = {\frac{\sqrt{2}}{2}A_{i}\sigma \quad {^{{({{\omega \quad t} - {kL}_{2}})}}.}}} & (3) \end{matrix}$

The resultant output is $\begin{matrix} {{A = {{r + s} = {\frac{\sqrt{2}}{2}A_{i}\left\{ {{\rho \quad ^{{- }\quad {kL}_{1}}} + {\sigma \quad ^{{- }\quad {kL}_{2}}}} \right\} ^{\quad \omega \quad t}}}},} & (4) \end{matrix}$

which may be rewritten as $\begin{matrix} \begin{matrix} {A = \quad {\frac{\sqrt{2}}{2}A_{i}{^{\quad \omega \quad t}\left\lbrack {^{\quad \frac{{- }\quad {k{({L_{1} + L_{2}})}}}{2}}{{^{{- }\quad \tan^{- 1}{\{{\frac{\rho \cdot \sigma}{\rho + \sigma}\quad \tan \quad \frac{k{({L_{1} \cdot L_{2}})}}{2}}\}}} \cdot}}} \right.}}} \\ {\quad {\sqrt{\rho^{2} + \sigma^{2} + {2\rho \quad \sigma \quad {\cos \quad\left\lbrack {k\left( {L_{1} - L_{2}} \right)} \right\rbrack}}}}} \end{matrix} & (5) \end{matrix}$

Now $\begin{matrix} {{\varphi = {{- \frac{k\left( {L_{1} - L_{2}} \right)}{2}} - {\tan^{- 1}\left\{ {\frac{\rho - \sigma}{\rho + \sigma}\quad \tan \quad \frac{k\left( {L_{1} - L_{2}} \right)}{2}} \right\}}}},\quad {and}} & (6) \\ {{{{\varphi}/{t}} = {- {\left( {k/2} \right)\left\lbrack {\frac{\left( {L_{1} - L_{2}} \right)}{t} + \frac{\left( {\rho^{2} - \sigma^{2}} \right)}{\rho^{2} + \sigma^{2} + {2\rho \quad \sigma \quad {\cos \quad\left\lbrack {k\left( {L_{1} - L_{2}} \right)} \right\rbrack}}}} \right\rbrack}}},} & (7) \\ {I = {\frac{1}{2}{I_{i}\left( {\rho^{2} + \sigma^{2} + {2\rho \quad \sigma \quad {\cos \quad\left\lbrack {k\left( {L_{1} - L_{2}} \right)} \right\rbrack}}} \right.}}} & (8) \\ {\frac{I}{t} = {\frac{1}{2}{I_{i}\left( {{- 2}\rho \quad \sigma \quad {{\sin \quad\left\lbrack {k\left( {L_{1} - L_{2}} \right)} \right\rbrack} \cdot k}\quad {\frac{\left( {L_{1} - L_{2}} \right)}{t}.}} \right.}}} & (9) \end{matrix}$

The chirp factor, as noted above, is defined as: $\begin{matrix} {\alpha \equiv {\frac{\frac{\varphi}{t}}{\left( \frac{1}{2I} \right)\frac{I}{t}}.}} & (10) \end{matrix}$

Recognizing that ρ²=1−σ², allows the expression for the chirp factor to be rewritten as: $\begin{matrix} \begin{matrix} {\alpha = \quad {\frac{1 - {2\quad \sigma^{2}}}{2\quad \sigma \sqrt{1 - \sigma^{2}}\quad {\sin \quad\left\lbrack {k\left( {L_{1} - L_{2}} \right)} \right\rbrack}} +}} \\ {\quad {\frac{1 + {2\quad \sigma \sqrt{1 - \sigma^{2}}\quad {\cos \quad\left\lbrack {k\left( {L_{1} - L_{2}} \right)} \right\rbrack}}}{2\quad \sigma \sqrt{1 - \sigma^{2}}\quad {\sin \quad\left\lbrack {k\left( {L_{1} - L_{2}} \right)} \right\rbrack}} \cdot {\frac{\frac{\left( {L_{1} + L_{2}} \right)}{t}}{\frac{\left( {L_{1} - L_{2}} \right)}{t}}.}}} \end{matrix} & (11) \end{matrix}$

Alternatively, the chirp factor may be expressed in terms of the power, P₁,P₂, in each waveguide arm 716, 718, recognizing that ρ²=P₁, and σ²=P₂, with P₁, being the power in waveguide arm 716 and P₂ being the power in waveguide arm 718, as: $\begin{matrix} \begin{matrix} {\alpha = \quad {\frac{\left( {1 - \frac{P_{2}}{P_{1}}} \right)}{2\quad \sqrt{\frac{P_{2}}{P_{1}}}\quad {\sin \quad\left\lbrack {k\left( {L_{1} - L_{2}} \right)} \right\rbrack}} +}} \\ {\quad {\frac{1 + \frac{P_{2}}{P_{1}} + {2\quad \sqrt{\frac{P_{2}}{P_{1}}}\quad {\cos \quad\left\lbrack {k\left( {L_{1} - L_{2}} \right)} \right\rbrack}}}{2\quad \sqrt{\frac{P_{2}}{P_{1}}}\quad {\sin \quad\left\lbrack {k\left( {L_{1} - L_{2}} \right)} \right\rbrack}} \cdot \frac{\frac{\left( {L_{1} + L_{2}} \right)}{t}}{\frac{\left( {L_{1} - L_{2}} \right)}{t}}}} \end{matrix} & (12) \end{matrix}$

Turning now to FIG. 8, a modulator 810 in accordance with the principles of the invention is shown. Integrated optic modulator 810 includes an optical waveguide 812 that is split by an optical splitter 814 into two waveguide arms 816, 818. Optical waveguide arms 816, 818 are rejoined with an optical coupler 820. FIG. 9 shows modulator 810 in cross section taken along lines 9—9. The modulator 810 is formed on a substrate 801 that is lithium niobate. As will be appreciated by those skilled in the art, substrate 801 may be of other material including, but not limited to GaAs. Optical waveguide arms 816, 818 are formed in substrate 801. Electrodes 822, 824, 826 are formed on substrate 801 proximate optical waveguide arms 816, 818. The distance between electrode 822 and electrode 824 is the same as the distance between electrode 824 and electrode 826, providing even gaps 828, 830 between electrode pairs. Electrodes 822 and 824 are of substantially equal effective length, l₂, proximate waveguide arm 818. Electrode 826 is configured so as to provide a different effective electrode length, l₁, proximate waveguide arm 816. The effective optical path lengths of the waveguide arms 816, 818 are L₁ and L₂, respectively. The path lengths are affected by the modulation voltage induced path length and a bias induced path length, L_(bias). The optical path lengths of the wave guide arms in the absence of modulation and bias are L₁₀ and L₂₀. From these identities,

L ₁ =L ₁₀ +γl ₁ V(t)+L_(bias), and  (13)

L ₂ =L ₂₀ −γl ₂ V(t)−L_(bias).  (14)

From the above, various portions of the other equations may be determined as follows:

L ₁ +L ₂ =L ₁₀ +L ₂₀ +γV(t)(l₁−l₂),  (15)

$\begin{matrix} {{\frac{\left( {L_{1} + L_{2}} \right)}{t} = {{\gamma \left( {l_{1} - l_{2}} \right)}\frac{V}{t}}},} & (16) \\ {{{L_{1} - L_{2}} = {L_{10} - L_{20} + {\gamma \quad {V(t)}\quad \left( {l_{1} + l_{2}} \right)} + {2L_{bias}}}},} & (17) \\ {{\frac{\left( {L_{1} - L_{2}} \right)}{t} = {{\gamma \left( {l_{1} + l_{2}} \right)}\frac{V}{t}}},} & (18) \\ {{k = \frac{{2\pi}\quad}{\lambda}},\quad {and}} & (19) \\ {{k\left( {L_{1} - L_{2}} \right)} \equiv {\varphi_{bias} + {\frac{\pi}{V_{\pi}}{{V(t)}.}}}} & (20) \end{matrix}$

For small signals, φ₀ is much smaller than 1. If the power ratio is defined as ${X \equiv \frac{P_{2}}{P_{1}}},$

then the chirp equation becomes: $\begin{matrix} {\alpha = {\frac{\left( {1 - X} \right)}{2\sqrt{X}{\sin \quad\left\lbrack \varphi_{bias} \right\rbrack}} + {\frac{\left( {l_{1} - l_{2}} \right)}{\left( {l_{1} + l_{2}} \right)} \cdot {\frac{\left. \left( {1 + X + {2\sqrt{X}\quad \cos \quad \varphi_{bias}}} \right. \right\rbrack}{2X\quad {\sin \quad\left\lbrack \varphi_{bias} \right\rbrack}}.}}}} & (21) \end{matrix}$

To understand the effect of varying the length of the electrodes, the following may be considered, If the electrodes are of equal length L₀, the phase shift is φ₀=2KL₀, where K contains all the various coefficients in the relevant equations including, but not limited to, the voltage and overlap coefficients. If one electrode is shortened by an amount “z” and the other is lengthened by an amount “w”, then

L _(e1) ≡L ₀ −z=l ₁,  (22)

and

Le ₂ ≡L ₀ +w=l ₂,  (23)

and

φ=K(L ₀ −z)+K(L ₀ +w)=2KL ₀ +K(w−z).  (24)

For a 10% increase in voltage (directly changing K) to produce the same phase shift, the equations may be solved to show that z=1+0.182L₀, and the modified electrode lengths are L_(e1)=0.818L₀−w, and L_(e2)=L₀+w. If electrode length alone is used to achieve a chirp parameter of α=−0.7, then ${{- 0.7} = \frac{- \left( {{2l} + {0.182L_{0}}} \right)}{1.818L_{0}}},$

yielding l=0.545L₀, so that L_(e1)=0.273L₀, and L_(e2)=1.545L₀.

The use of power adjusting between the two waveguide arms 816, 818 may also be used. Using the above values for L_(e1) and L_(e2) in the chirp parameter equation provides: $\begin{matrix} {\alpha = {\frac{1 - X}{2\sqrt{X}\sin \quad \left( \varphi_{b} \right)} - {0.7\quad {\frac{\left( {1 + x + {2\sqrt{X}\cos \quad \left( \varphi_{b} \right)}} \right)}{2\sqrt{X}\sin \quad \left( \varphi_{b} \right)}.}}}} & (25) \end{matrix}$

If it is desired to adjust the power to achieve ±0.2 chirp, and assuming φ_(b)=π/2, the first term in the equation dominates and $\alpha = {{\pm 0.2} = {\frac{1 - X}{2\sqrt{X}}.}}$

Solving for X, yields X=1.488, 0.672. With equal power levels in both waveguide arms, i.e., X=1.0 or P₁=P₂, a chirp factor of α=−0.7 is obtained. With X =1.488, a chirp factor of α=−0.9 is obtained. With X =0.672, a chirp factor of α=−0.5 is obtained. At either power ratio, an on/off ratio of less than −20 dB is obtained.

From the above analysis, chirp, α, and extinction or on-off ratio data has been calculated for different electrode length ratios, L_(e2)/L_(e1), bias deviation from π/2 and, the power ratio, X between the waveguide arms. The data is set forth in TABLE 1.

TABLE 1 electrode bias length deviation power on/off ratio from π/2 ratio chirp ratio 2.67 −0.05 π 1.60 −0.78569 −14.2231 2.67 −0.05 π 1.65 −0.80347 −14.0227 2.67 −0.05 π 1.70 −0.82088 −13.8258 2.67 −0.05 π 1.75 −0.83794 −13.6331 2.67 −0.05 π 1.80 −0.85468 −13.445 2.67 −0.05 π 1.85 −0.87111 −13.2617 2.67 −0.05 π 1.90 −0.88725 −13.0834 2.67 −0.05 π 1.95 −0.9031 −12.9101 2.67 −0.05 π 2.00 −0.91869 −12.7418 2.67 −0.025 π 1.60 −0.74283 −17.0438 2.67 −0.025 π 1.65 −0.76044 −16.6611 2.67 −0.025 π 1.70 −0.77769 −16.2999 2.67 −0.025 π 1.75 −0.79459 −15.9589 2.67 −0.025 π 1.80 −0.81118 −15.6366 2.67 −0.025 π 1.85 −0.82746 −15.3316 2.67 −0.025 π 1.90 −0.84344 −15.0427 2.67 −0.025 π 1.95 −0.85915 −14.7687 2.67 −0.025 π 2.00 −0.87459 −14.5085 2.67 0 1.60 −0.70483 −18.639 2.67 0 1.65 −0.72239 −18.0935 2.67 0 1.70 −0.73959 −17.5961 2.67 0 1.75 −0.75644 −17.1398 2.67 0 1.80 −0.77298 −16.719 2.67 0 1.85 −0.7892 −16.3292 2.67 0 1.90 −0.80514 −15.9666 2.67 0 1.95 −0.8208 −15.6281 2.67 0 2.00 −0.8362 −15.311 2.67 0.025 π 1.60 −0.6712 −18.6126 2.67 0.025 π 1.65 −0.68881 −18.0671 2.67 0.025 π 1.70 −0.70606 −17.5698 2.67 0.025 π 1.75 −0.72297 −17.1135 2.67 0.025 π 1.80 −0.73955 −16.6928 2.67 0.025 π 1.85 −0.75583 −16.303 2.67 0.025 π 1.90 −0.77182 −15.9404 2.67 0.025 π 1.95 −0.78753 −15.602 2.67 0.025 π 2.00 −0.80297 −15.285 2.67 0.05 π 1.60 −0.64155 −18.5329 2.67 0.05 π 1.65 −0.65932 −17.9876 2.67 0.05 π 1.70 −0.67674 −17.4904 2.67 0.05 π 1.75 −0.6938 −17.0343 2.67 0.05 π 1.80 −0.71054 −16.6137 2.67 0.05 π 1.85 −0.72697 −16.2241 2.67 0.05 π 1.90 −0.7431 −15.8617 2.67 0.05 π 1.95 −0.75896 −15.5234 2.67 0.05 π 2.00 −0.77455 −15.2066 2.67 0.075 π 1.60 −0.61652 −18.3991 2.67 0.075 π 1.65 −0.63367 −17.8541 2.67 0.075 π 1.70 −0.65136 −17.3571 2.67 0.075 π 1.75 −0.66869 −16.9013 2.67 0.075 π 1.80 −0.68569 −16.481 2.67 0.075 π 1.85 −0.70238 −16.0917 2.67 0.075 π 1.90 −0.71877 −15.7295 2.67 0.075 π 1.95 −0.73488 −15.3915 2.67 0.075 π 2.00 −0.75071 −15.075 2.67 0.1 π 1.60 −0.59326 −18.2094 2.67 0.1 π 1.65 −0.61172 −17.6648 2.67 0.1 π 1.70 −0.6298 −17.1682 2.67 0.1 π 1.75 −0.64752 −16.7128 2.67 0.1 π 1.80 −0.6649 −16.2929 2.67 0.1 π 1.85 −0.68197 −15.904 2.67 0.1 π 1.90 −0.69872 −15.423 2.67 0.1 π 1.95 −0.71519 −15.2047 2.67 0.1 π 2.00 −0.73138 −14.8886 2.67 0.125 π 1.60 −0.57422 −17.9615 2.67 0.125 π 1.65 −0.59343 −17.4174 2.67 0.125 π 1.70 −0.61204 −16.9214 2.67 0.125 π 1.75 −0.63028 −16.4665 2.67 0.125 π 1.80 −0.64818 −16.0471 2.67 0.125 π 1.85 −0.66574 −15.6588 2.67 0.125 π 1.90 −0.68299 −15.2977 2.67 0.125 π 1.95 −0.69994 −14.9607 2.67 0.125 π 2.00 −0.71661 −14.6452 2.5 −0.05 π 1.60 −0.75396 −14.2231 2.5 −0.05 π 1.65 −0.77163 −14.0227 2.5 −0.05 π 1.70 −0.78894 −13.8258 2.5 −0.05 π 1.75 −0.8059 −13.6331 2.5 −0.05 π 1.80 −0.82253 −13.445 2.5 −0.05 π 1.85 −0.83884 −13.2617 2.5 −0.05 π 1.90 −0.85486 −13.0834 2.5 −0.05 π 1.95 −0.8706 −12.9101 2.5 −0.05 π 2.00 −0.88607 −12.7418 2.5 0 1.60 −0.66763 −18.639 2.5 0 1.65 −0.69509 −18.0935 2.5 0 1.70 −0.71218 −17.5961 2.5 0 1.75 −0.72893 −17.1398 2.5 0 1.80 −0.74536 −16.719 2.5 0 1.85 −0.76147 −16.3292 2.5 0 1.90 −0.7773 −15.9666 2.5 0 1.95 −0.79284 −15.6281 2.5 0 2.00 −0.80812 −15.311 2.5 0.05 π 1.60 −0.6182 −18.5329 2.5 0.05 π 1.65 −0.63587 −17.9876 2.5 0.05 π 1.70 −0.65318 −17.4904 2.5 0.05 π 1.75 −0.67014 −17.0343 2.5 0.05 π 1.80 −0.68677 −16.6137 2.5 0.05 π 1.85 −0.70308 −16.2241 2.5 0.05 π 1.90 −0.71911 −15.8617 2.5 0.05 π 1.95 −0.73484 −15.5234 2.5 0.05 π 2.00 −0.75032 −15.2066 2.5 0.1 π 1.60 −0.57325 −18.2094 2.5 0.1 π 1.65 −0.59161 −17.6648 2.5 0.1 π 1.70 −0.60959 −17.1682 2.5 0.1 π 1.75 −0.62719 −16.7128 2.5 0.1 π 1.80 −0.64446 −16.2929 2.5 0.1 π 1.85 −0.66141 −15.904 2.5 0.1 π 1.90 −0.67805 −15.423 2.5 0.1 π 1.95 −0.69439 −15.2047 2.5 0.1 π 2.00 −0.71046 −14.8886 2.0 −0.05 π 1.60 −0.63977 −14.2231 2.0 −0.05 π 1.65 −0.65708 −14.0227 2.0 −0.05 π 1.70 −0.67402 −13.8258 2.0 −0.05 π 1.75 −0.69059 −13.6331 2.0 −0.05 π 1.80 −0.70682 −13.445 2.0 −0.05 π 1.85 −0.72274 −13.2617 2.0 −0.05 π 1.90 −0.73835 −13.0834 2.0 −0.05 π 1.95 −0.75367 −12.9101 2.0 −0.05 π 2.00 −0.76872 −12.7418 2.0 0 1.60 −0.57975 −18.639 2.0 0 1.65 −0.59685 −18.0935 2.0 0 1.70 −0.61357 −17.5961 2.0 0 1.75 −0.62994 −17.1398 2.0 0 1.80 −0.64597 −16.719 2.0 0 1.85 −0.66169 −16.3292 2.0 0 1.90 −0.67711 −15.9666 2.0 0 1.95 −0.69224 −15.6281 2.0 0 2.00 −0.70711 −15.311 2.0 0.05 π 1.60 −0.53418 −18.5329 2.0 0.05 π 1.65 −0.55149 −17.9876 2.0 0.05 π 1.70 −0.56843 −17.4904 2.0 0.05 π 1.75 −0.585 −17.0343 2.0 0.05 π 1.80 −0.60123 −16.6137 2.0 0.05 π 1.85 −0.61715 −16.2241 2.0 0.05 π 1.90 −0.63276 −15.8617 2.0 0.05 π 1.95 −0.64808 −15.5234 2.0 0.05 π 2.00 −0.66313 −15.2066 2.0 0.1 π 1.60 −0.50128 −18.2094 2.0 0.1 π 1.65 −0.51926 −17.6648 2.0 0.1 π 1.70 −0.53684 −17.1682 2.0 0.1 π 1.75 −0.55405 −16.7128 2.0 0.1 π 1.80 −0.57091 −16.2929 2.0 0.1 π 1.85 −0.58744 −15.904 2.0 0.1 π 1.90 −0.60365 −15.423 2.0 0.1 π 1.95 −0.61956 −15.2047 2.0 0.1 π 2.00 −0.63519 −14.8886

From the above analysis and data, it is apparent that a variable chirp modulator may be constructed in accordance with the invention in which the electrode length ratio, the bias and the power ratio may be varied to influence both the chirp and the extinction or On/off ratio. In accordance with the principles of the invention, a variable chirp Mach Zehnder Interferometer type modulator is obtained by selecting an initial modulator design with uneven modulation between the two modulator waveguide arms by selecting a modulation ratio of 0.25, for example, to achieve a chirp parameter of α=−0.6, as a baseline.

The chirp parameter value can then be adjusted from the baseline by:

1. Changing the power ratio γ=P₁/(P₁+P₂) between the two arms of the modulator. The power ratio may be changed with a tunable attenuator in one arm of the modulator; or

2. Moving the bias point away from quadrature by applying an offset DC bias; or

3. Combining both 2. and 3. to obtain a larger chirp range.

Advantageously, a chirp modulator in accordance with the invention can be realized with an X-cut or Z-cut substrate. In addition, a chirp value of −0.7 is achieved with an adjustable chirp range of up to ±0.25 or more with an extinction ratio of better than 15 dB. The impact of V_(π)can be compensated with longer electrodes in the modulator.

In an implementation of a modulator in which an on/off ratio of −14 dB is desired, and the power between the two waveguide arms is not balanced, the power ratio x=4/9, and 9/4. Setting the value for negative chirp at −0.9, a length ratio of $\frac{L_{e2}}{L_{e1}} = {\frac{l_{2}}{l_{1}} = 2.61}$

is obtained. If it is desired to obtain the same phase shift for both a configuration of equal length electrodes and un-balanced length electrodes, the following calculations can be made. For equal length electrodes φ₀=2KL₀ and for the unbalanced electrode case φ=2Kl_(1+K(l) ₂−l₁)=3.61Kl₁. Equating the two cases yields l₁=0.554L₀ and l₂=1.446L₀. In this embodiment, the electrode length of the longer electrode is approximately 45% longer than the equal length electrodes, whereas, for balanced power, the electrode length of the longer electrode is about 55% greater that the equal length electrodes.

Utilizing the foregoing analysis, other embodiments of the invention have been developed.

Turning now to FIG. 10, a modulator 1010 in accordance with the principles of the invention is shown. Integrated optic modulator 1010 includes an optical waveguide 1012 that is split by an optical splitter 1014 into two waveguide arms 1016, 1018. Optical waveguide arms 1016, 1018 are rejoined with an optical coupler 1020. FIG. 11 shows modulator 1010 in cross section taken along lines 11—11. The modulator 1010 is formed on a substrate 1001 that is lithium niobate. As will be appreciated by those skilled in the art, substrate 1001 may be of other material including, but not limited to GaAs. Optical waveguide arms 1016, 1018 are formed in substrate 1001. Electrodes 1022, 1024, 1026 are formed on substrate 1001 proximate optical waveguide arms 1016, 1018. The distance between electrode 1022 and electrode 1024 is the same as the distance between electrode 1024 and portions 1027 of electrode 1026, providing even gaps 1028, 1030 between electrode pairs. Electrodes 1022 and 1024 are of substantially equal effective length, l₂, proximate waveguide arm 1016. Electrode 1026 is configured so as to provide a different effective electrode length, l₁, proximate waveguide arm 1018. The particular configuration shown in FIGS. 10 and 11 is such that electrode 1026 includes a plurality of portions 1027, numbering two in the specific embodiment shown, that have a combined length of l₁ proximate waveguide arm 1018. The remaining portion or portions 1029 of electrode 1026 are spaced apart from waveguide arm 1018 so as to have minimal modulation effect. A variable attenuator 1040 is formed in waveguide arm 1018 and includes electrodes 1041, 1042. The variable attenuator 1040 is utilized to provide unequal power splitting in the two waveguide arms 1016, 1018. Bias electrodes 1050, 1051, 1052 are also provided.

Turning now to FIG. 12, a modulator 1210 in accordance with the principles of the invention is shown. Integrated optic modulator 1210 includes an optical waveguide 1212 that is split by an optical splitter or tunable coupler 1214 into two waveguide arms 1216, 1218. Optical waveguide arms 1216, 1218 are rejoined with an optical coupler 1220. FIG. 13 shows modulator 1210 in cross section taken along lines 13—13 and FIG. 14 shows modulator 1210 in cross section taken along lines 14—14. Modulator 1210 is formed on a substrate 1201 that is lithium niobate. As will be appreciated by those skilled in the art, substrate 1201 may be of other material including, but not limited to GaAs. Optical waveguide arms 1216, 1218 are formed in substrate 1201. Electrodes 1222, 1224, 1226 are formed on substrate 1201 proximate optical waveguide arms 1216, 1218. The distance or gap 1228 between electrode the electrode pair comprising electrode 1222 and electrode 1224 is the same as the distance or gap 1230 between the electrode pair comprising electrode 1224 and electrode 1226. Electrodes 1222 and 1224 are of substantially equal effective length, l₂, proximate waveguide arm 1216. Electrode 1226 and optical waveguide arm 1218 are cooperatively configured so as to provide a different effective electrode length, l₁, proximate waveguide arm 1218. The particular configuration shown in FIGS. 12, 13 and 14 is such that waveguide arm 1218 includes a first portion 1219 that is disposed between electrodes 1224, 1226 and a second portion 1221 that is offset from portion 1219 and disposed out of the area of substrate 1201 that is affected by a modulation voltage impressed across electrodes 1226, 1128. The amount of offset x1 between portion 1219 and portion 1221 provided by offset portion 1223 is matched in waveguide arm 1216 by portion 1215. The offset portion 1215 is provided in waveguide arm 1216 to provide for equal optical path lengths in the two waveguide arms 1216 and 1218. A variable attenuator 1240 is formed in waveguide arm 1218 and includes electrodes 1241, 1242. Variable attenuator 1240 is utilized to provide unequal power splitting in the two waveguide arms 1216, 1218. Bias electrodes 1250, 1252, 1254 are also provided and utilized to provide bias. Also shown if FIG. 12 is a variable coupler 1270 comprising electrodes 1271, 1272, 1273. Typically either variable coupler 1270 or variable attenuator 1240 is used to control the power split between waveguide arms 1216, 1218.

The invention has been described in terms of several embodiments. It will be apparent to those skilled in the art that various changes and modifications may be made to the embodiments shown and described without departing from the spirit or scope of the invention. It is intended that the invention includes all such changes and modifications and other changes and modifications that are not specifically mentioned. It is further intended that the invention not be limited in scope to the embodiments shown and described, but that the invention is limited in scope only by the claims appended hereto. 

What is claimed is:
 1. An optical modulator, comprising: an optical waveguide, said optical waveguide splitting for part of its length into first and second waveguide arms, said waveguide arms recombining to an output waveguide portion; a first electrode pair proximate said first waveguide arm and arranged with respect to each other and said first waveguide arm to subject a first optical length of said first waveguide to a first modulating electric field; a second electrode pair proximate said second waveguide arm and arranged with respect to each other and to said second waveguide arm to subject a first optical length of said second waveguide arm to a second modulating electric field, said second electrode pair being shorter than said first electrode pair, the lengths of said first electrode pair and said second electrode pair being selected to provide a predetermined amount of chirp; and means for providing unequal optical power in said first and said second waveguide arms.
 2. An optical modulator in accordance with claim 1, comprising: said means providing less power in said second waveguide arm than provided in said first waveguide arm.
 3. An optical modulator in accordance with claim 2, comprising: a first pair of bias electrodes disposed proximate said first waveguide arm; and a second pair of bias electrodes disposed proximate said second waveguide arm.
 4. An optical modulator in accordance with claim 1, comprising: a tunable attenuator disposed in said second waveguide arm to vary the amount of chirp produced by said modulator.
 5. An optical modulator in accordance with claim 4, comprising: a tunable “Y” coupling said optical waveguide to said first and second waveguide arms, said tunable “Y” being adjustable to control the power split between said first and said second waveguide arms.
 6. An optical modulator in accordance with claim 1, comprising: a tunable “Y” coupling said optical waveguide to said first and second waveguide arms, said tunable “Y” being adjustable to control the power split between said first and said second waveguide arms.
 7. An optical modulator in accordance with claim 6, comprising: a first bias electrode pair disposed proximate said first waveguide arm; and a second bias electrode pair disposed proximate said second waveguide arm.
 8. An optical modulator in accordance with claim 7, wherein: said first and said second bias electrode pairs share a common electrode.
 9. An optical modulator in accordance with claim 1, wherein: said first electrode pair are spaced apart by a first gap; said second electrode pair are spaced apart by a second gap; and said first gap and said second gap are substantially equal in width.
 10. An optical modulator in accordance with claim 9, comprising: said first optical length of said first waveguide arm is disposed under said first gap; and said first optical length of said second waveguide arm is disposed under said second gap.
 11. An optical modulator in accordance with claim 1, comprising: an optical waveguide coupler for coupling said first and said second waveguide arms together to combine the outputs of said first and said second waveguide arms.
 12. An optical modulator comprising: an optical waveguide; first and second optical waveguide arms; an optical apparatus coupled to said waveguide and coupled to said first and second waveguide arms; a common electrode; disposed between said first and second waveguide arms; a first electrode disposed on one side of said common electrode and spaced apart therefrom to produce a first gap; a second electrode disposed on another side of said common electrode and spaced apart therefrom to produce a second gap; said first waveguide arm comprising a first portion positioned proximate said first gap; said second waveguide arm comprising a first portion positioned proximate said second gap and a second portion positioned a distance away from said second gap; said first electrode having a first length, said second electrode having a second length, said first length and said second length having a predetermined relationship.
 13. An optical modulator in accordance with claim 12, comprising: said predetermined relationship determines a nominal value of chirp for said modulator.
 14. An optical modulator in accordance with claim 13, wherein: said first waveguide arm is positioned in a plane under said first gap; and said second waveguide arm is positioned in a plane under said second gap.
 15. An optical modulator in accordance with claim 16, wherein: said first waveguide arm has a first total optical length; said second waveguide arm has a second total optical length; and said first total optical length is substantially equal to said second total optical length.
 16. An optical modulator in accordance with claim 15, comprising: means for controlling the amount of optical power from said optical waveguide that is provided to said first waveguide arm and to said second waveguide arm to vary said chirp from said nominal value of chirp.
 17. An optical modulator in accordance with claim 16, wherein: said power controlling means comprises a tunable attenuator disposed in one of said first or said second waveguide arms.
 18. An optical modulator in accordance with claim 17, wherein: said tunable attenuator is disposed in said second waveguide arm.
 19. An optical modulator in accordance with claim 18, wherein: said power controlling means comprises a tunable “y” operable to control the amount of power provided to said first waveguide arm and to said second waveguide arm.
 20. An optical modulator, comprising: an optical waveguide, said optical waveguide splitting for part of its length into first and second waveguide arms, said waveguide arms recombining to an output waveguide portion; a first electrode proximate said first waveguide arm to subject a first optical length of said first waveguide to a first modulating electric field; a second electrode proximate said second waveguide arm to subject a first optical length of said second waveguide arm to a second modulating electric field, said second electrode being shorter than said first electrode, the lengths of said first electrode and said second electrode being selected to provide a predetermined amount of chirp; and apparatus in said optical waveguide providing for different optical power levels in said first and said second waveguide arms to control the amount of chirp.
 21. An optical modulator in accordance with claim 20, comprising: said apparatus providing less power in said second waveguide arm than provided in said first waveguide arm.
 22. An optical modulator in accordance with claim 21, comprising: a first pair of bias electrodes disposed proximate said first waveguide arm; and a second pair of bias electrodes disposed proximate said second waveguide arm.
 23. An optical modulator in accordance with claim 22, comprising: a tunable attenuator disposed in said second waveguide arm to vary the amount of chirp produced by said modulator.
 24. An optical modulator in accordance with claim 23, comprising: a tunable “Y” coupling said optical waveguide to said first and second waveguide arms, said tunable “Y” being adjustable to control the power split between said first and said second waveguide arms.
 25. An optical modulator in accordance with claim 20, comprising: a tunable “Y” coupling said optical waveguide to said first and second waveguide arms, said tunable “Y” being adjustable to control the power split between said first and said second waveguide arms.
 26. An optical modulator in accordance with claim 25, comprising: a first bias electrode disposed proximate said first waveguide arm; and a second bias electrode disposed proximate said second waveguide arm.
 27. An optical modulator in accordance with claim 26, wherein: said first and said second bias electrodes share a common electrode.
 28. An optical modulator in accordance with claim 20, wherein: said first electrode and said common electrode are spaced apart by a first gap; said second electrode and said common electrode are spaced apart by a second gap, and said first gap and said second gap are substantially equal in width.
 29. An optical modulator in accordance with claim 28, comprising: said first optical length of said first waveguide arm is disposed under said first gap; and said first optical length of said second waveguide arm is disposed under said second gap.
 30. An optical modulator in accordance with claim 20, comprising: an optical waveguide coupler for coupling said first and said second waveguide arms together to combine the outputs of said first and said second waveguide arms.
 31. An optical modulator comprising: an optical waveguide; first and second optical waveguide arms; an optical apparatus coupled to said waveguide and coupled to said first and second waveguide arms; a first electrode; a second electrode; said first waveguide arm comprising a first portion positioned proximate said first electrode, said second waveguide arm comprising a first portion positioned proximate said second electrode; said first electrode having a first length, said second electrode having a second length, said first length and said second length having a predetermined relationship, and. said predetermined relationship determines a nominal value of chirp for said modulator.
 32. An optical modulator in accordance with claim 31, wherein; said first waveguide arm has a first total optical length; said second waveguide arm has a second total optical length; and said first total optical length is substantially equal to said second total optical length.
 33. An optical modulator in accordance with claim 32, comprising: means for controlling the amount of optical power from said optical waveguide that is provided to said first waveguide arm and to said second waveguide arm to vary said chirp from said nominal value of chirp.
 34. An optical modulator in accordance with claim 33, wherein: said power controlling means comprises a tunable attenuator disposed in one of said first or said second waveguide arms.
 35. An optical modulator in accordance with claim 34, wherein: said tunable attenuator is disposed in said second waveguide arm.
 36. An optical modulator in accordance with claim 35, wherein: said power controlling means comprises a tunable “y” operable to control the amount of power provided to said first waveguide arm and to said second waveguide arm. 